Abstract
We consider the problems of online and stochastic packet queuing in a distributed system of n nodes with queues, where the communication between the nodes is done via a multiple access channel. In each round, an arbitrary number of packets can be injected into the system, each to an arbitrary node’s queue. Two measures of performance are considered: the total number of packets in the system, called the total load, and the maximum queue size, called the maximum load. In the online setting, we develop a deterministic algorithm that is asymptotically optimal with respect to both complexity measures, in a competitive way. More precisely, the total load of our algorithm is bigger then the total load of any other algorithm, including centralized offline solutions, by only O(n 2), while the maximum queue size of our algorithm is at most n times bigger than the maximum queue size of any other algorithm, with an extra additive O(n). The optimality for both measures is justified by proving the corresponding lower bounds. Next, we show that our algorithm is stochastically optimal for any expected injection rate smaller or equal to 1. To the best of our knowledge, this is the first solution to the stochastic queuing problem on a multiple access channel that achieves such optimality for the (highest possible) rate equal to 1.
Supported by MNiSW grant number N N206 368839, 2010-2013. The work of the second and the fourth author was supported by the Engineering and Physical Sciences Research Council [grant number EP/G023018/1]. The third author is supported by grant 2010/342643 of the Institute of Mathematics and Computers Science of the Wroclaw University of Technology.
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Bienkowski, M., Jurdzinski, T., Korzeniowski, M., Kowalski, D.R. (2012). Distributed Online and Stochastic Queuing on a Multiple Access Channel. In: Aguilera, M.K. (eds) Distributed Computing. DISC 2012. Lecture Notes in Computer Science, vol 7611. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33651-5_9
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DOI: https://doi.org/10.1007/978-3-642-33651-5_9
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